Card Counting

Most casino players think of card counting as an esoteric skill requiring feats of superhuman memory and computer-like mathematical prowess. The reality is that thousands of players know how to count cards in blackjack, and most of them have average intelligence. Counting cards is one of the only ways to get a consistent mathematical edge over a casino, but it does require significant amounts of dedicated practice and study before you can reliably count on that edge.

Entire books and websites have been written about this particular method of advantage gambling. The purpose of this page isn’t to provide a comprehensive guide to card counting, but it does aim to provide a detailed discussion of the basics.

Edward Thorp’s Beat the Dealer

Edward Thorp published Beat the Dealer in 1962, and this date is considered the genesis of advantage play at blackjack. According to multiple sources, including Thorp, but also according to Stanford Wong’s Big Book of Blackjack and Andrew Brisman’s Mensa Guide to Casino Gambling, early blackjack players intuitively gained an edge over the casino game by using primitive counting techniques. The idea wasn’t popularized or a concern of the casinos until the publication of Thorp’s book, though.

The casinos’ reaction to the publication of Beat the Dealer was a comical overreaction. They were afraid that mobs of blackjack players would start taking them for all they were worth, and so they made dramatic changes to their house rules in order to make it impossible to get an edge. Before Beat the Dealer, it was common for a casino to deal blackjack from a single deck and to deal all the way to the bottom of that deck. This practice was eliminated, and several other rules designed to eliminate a counter’s edge were put into place. This backfired, though—the rules had become so restrictive that even the people who weren’t counting stopped playing blackjack.

The reality is that the casinos probably didn’t have much to worry about in the 1960s. Thorp’s methods were a little on the unwieldy side, and even though blackjack was the fresh new “beatable” casino game for intelligent players, most players didn’t study or practice enough to actually get an edge. What had happened instead was that a lot of clueless players started playing, which probably made more money for the casinos’ blackjack tables than they would have before. In fact, one of the reasons that blackjack makes up 50% of a casino’s table game revenue is that it’s considered a game that an intelligent player can beat.

Why Does Counting Cards Work

In almost all casino games, each wager is made on an independent event, so there’s no way to overcome the game’s insurmountable mathematical edge. Blackjack is an exception, though—the odds change with every card that’s dealt in a blackjack game. For example, if you spin the wheel on a roulette game, and you wager on black, then 18 of the possible outcomes are winners. On your second spin, that same wager on black has the same number of potential winning outcome: 18. In blackjack, though, the cards that have been dealt change the number of potential outcomes. For example, if all four aces have been dealt, the probability of being dealt a natural 21 have been reduced to 0%. (You can’t get a natural blackjack without an ace in the deck.)

As a general rule, a deck with a lot of high cards (tens and aces) left in it is better for the player, while a deck with a lot of low cards (twos, threes, fours, fives, and sixes) is better for the dealer. When the deck is rich in high cards, the player has a better chance of being dealt a natural, which pays out at 3 to 2. Perceptive readers might notice that the dealer also has a better chance of getting a blackjack, too, but the dealer doesn’t get a 3 to 2 payout—only the player does.

Some of the advantage from counting cards is had from making some simple basic strategy changes. For example, in a deck that’s rich in tens and aces, it makes sense to avoid hitting stiff hands. The dealer doesn’t get to make this decision; the dealer has to hit a certain total and stand on a certain total, regardless of whether or not it’s the right play given the composition of the deck.

Another strategy change with a deck that’s composed more than 2/3 of high cards is to take insurance. Normally that’s a sucker bet with a huge negative expectation, but not when you’re counting cards and know the score.

When the deck is rich in lower ranked cards, the dealer is less likely to bust, making it harder for the player to win that way. It’s also less likely that a player will be dealt a natural when there are still a lot of low cards in the deck.

The bulk of the player’s advantage comes from betting more when the deck is rich in high cards and betting less when the deck is rich in low cards. The 3 to 2 payout for a blackjack is where the counter gets most of his edge. Most counters range their bets from 1 to 5 units based on how favorable the count is, but some even range their bets from 1 to 10 units. The casinos watch players who ranger their bets, though, so don’t be surprised if you don’t get some “heat” from the casino. Professional blackjack players use various means of “camouflage” to disguise the fact that they’re counting, and they even sometimes work in teams. You can see examples of camouflage in action in the movie 21, which shows one way in which a team takes advantage of a hot deck.

How Card Counting Works

You don’t have to memorize all the cards that have been played in order to count cards. Card counting uses a heuristic method of tracking the ratio of high cards to low cards. The Hi-Lo system is one of the most common ways of doing this. It assigns the following values to the following cards:

  • 2,3,4,5,6 = +1
  • 10, J, Q, K, A = -1
  • The other cards (7,8,9) =0

You start your count at 0, and then as each card is dealt, you adjust the account by either adding 1 or subtracting 1. That running total is called the “running count”, but the running count alone isn’t enough to make you profitable. Most casinos use multiple decks, so you have to convert the running count into what’s called the “true count” in order to make the correct decisions.

In order to calculate the true count, you first estimate how many decks are still left in the shoe (the device which holds the cards for the blackjack dealer). Then you divide the running count by the number of decks left. For example, if your running count is +4, and you estimate that 4 decks remain in the shoe, then the true count is +1.

The higher the count, the more you bet. Competent counters can reduce the house edge, in which the player has a disadvantage of 1% or 2% to the casino, to an edge of 0.5% to 1.5% over the casino. If you’re playing for $20 per hand on average, and you play 100 hands per hour, then you’re putting $2000 per hour into action. With a 1% advantage, that means you can expect, in the long run, to earn $20 per hour for your efforts.

Keep in mind that this number isn’t guaranteed, either. In the short run, anything can happen, and even card counters with large bankrolls can go broke quickly if luck turns against them. Besides short term fluctuations in the mathematics of the game, casinos will often refuse to let you play blackjack. In Atlantic City, it’s illegal for a casino to bar a player from blackjack, but they’ve made the rules there so tight that it’s practically impossible to get an edge over the casino.

Other card counting strategies offer varying degrees of complexity in exchange for varying degrees of accuracy. Most players look for a balance of practicality and playability when choosing a system. Other pages on our site look at the specifics of these other counting techniques.